(a) Solve [tex]a^T~a~\hat{x} = a^T~b[/tex] to show that [tex]\hat{x}[/tex]is the mean (the average) of the b’s.(b) Find [tex]e = b - a \hat{x}[/tex] and the variance [tex]||e||^2[/tex] and the standard deviation [tex]||e||[/tex].(c) The horizontal line [tex]\hat{b} = 3[/tex] is closest to b = (1, 2, 6). Check that p = (3, 3 3) is perpendicular to e and find the 3 by 3 projection matrix P.